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-cos(1/x)/x^2
Limit of the function/ -cos(1/x)/x^2

Limit of the function -cos(1/x)/x^2

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You have entered [src] 
     /    /  1\ \
     |-cos|1*-| |
     |    \  x/ |
 lim |----------|
x->0+|     2    |
     \    x     /
lim⁡x→0+((−1)cos⁡(1⋅1x)x2)\lim_{x \to 0^+}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) 
Limit((-cos(1/x))/(x^2), x, 0)
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
02468-8-6-4-2-1010-100100
Plot the graph
One‐sided limits [src] 
     /    /  1\ \
     |-cos|1*-| |
     |    \  x/ |
 lim |----------|
x->0+|     2    |
     \    x     /
lim⁡x→0+((−1)cos⁡(1⋅1x)x2)\lim_{x \to 0^+}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) 
oo*sign(<-1, 1>)
∞sign⁡(⟨−1,1⟩)\infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)} 
= 3.96548889008278e-74
     /    /  1\ \
     |-cos|1*-| |
     |    \  x/ |
 lim |----------|
x->0-|     2    |
     \    x     /
lim⁡x→0−((−1)cos⁡(1⋅1x)x2)\lim_{x \to 0^-}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) 
oo*sign(<-1, 1>)
∞sign⁡(⟨−1,1⟩)\infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)} 
= 3.96548889008278e-74
= 3.96548889008278e-74
Rapid solution [src] 
oo*sign(<-1, 1>)
∞sign⁡(⟨−1,1⟩)\infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→0−((−1)cos⁡(1⋅1x)x2)=∞sign⁡(⟨−1,1⟩)\lim_{x \to 0^-}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
More at x→0 from the left
lim⁡x→0+((−1)cos⁡(1⋅1x)x2)=∞sign⁡(⟨−1,1⟩)\lim_{x \to 0^+}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = \infty \operatorname{sign}{\left(\left\langle -1, 1\right\rangle \right)}
lim⁡x→∞((−1)cos⁡(1⋅1x)x2)=0\lim_{x \to \infty}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = 0
More at x→oo
lim⁡x→1−((−1)cos⁡(1⋅1x)x2)=−cos⁡(1)\lim_{x \to 1^-}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = - \cos{\left(1 \right)}
More at x→1 from the left
lim⁡x→1+((−1)cos⁡(1⋅1x)x2)=−cos⁡(1)\lim_{x \to 1^+}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = - \cos{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞((−1)cos⁡(1⋅1x)x2)=0\lim_{x \to -\infty}\left(\frac{\left(-1\right) \cos{\left(1 \cdot \frac{1}{x} \right)}}{x^{2}}\right) = 0
More at x→-oo
Numerical answer [src] 
3.96548889008278e-74
3.96548889008278e-74
The graph
Limit of the function -cos(1/x)/x^2
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